The DM, when setting up his campaign, must decide how much magic there is in the world—not just magical items, but magical monsters, spells, and effects of any sort.
Magical World[]
In a warrior-oriented campaign where magic exists at the normal AD&D® game limits, magic is considered a scary thing which normal people don't appreciate at all. Most wizards encountered in the campaign will be villains. The ones who are friends of the PCs are mostly low-powered (low-level).
This follows the pattern of many sword-and-sorcery fiction series, where each story's resolution comes down to a contest between the hero and his fighting prowess vs. a dastardly wizard or magical creature and his spells.
In such a campaign, the DM will have to decide whether any player-character can be a multi-class or dual-class hero with Wizard or Priest spells. It's all right to have Ranger and Paladin characters, as they only acquire their spells slowly, and after many experience levels... but the more magically potent wizards and priests pose a bigger problem. Their magic is too handy and too dependable; the DM has to make his magical villains even more powerful in order to cope. In a campaign where PCs can't be priests or wizards, a much lower-level magical villain will be much more effective against them.
For these reasons, if you're going to try running a warrior-oriented campaign for the first time, we recommend that you not allow PCs to be priests or wizards. You can always choose to add the option later on... but if you find that you like the non-magical warrior arrangement, it's not so easy to remove the PCs' magical abilities from a campaign where you've already allowed them.
Mostly Non-Magical World[]
In a world where there's very little magic, no PC can learn spells. This means that no player-character can take a Priest or Wizard class as his character profession, or even as one of a dual-class or multi-class character's professions.
In such a campaign, characters can still be Rangers and Paladins. Even they can't learn spells... but they still get their other special abilities.
Paladins still have the abilities of detecting evil, +2 to saving throws, immunity to disease, healing by laying on hands, aura of protection, turn undead, devils, and demons, and calling of war horse; he can use the special abilities of a holy sword in the unlikely event he can find one. All the Paladin limitations still apply.
Rangers still have their abilities of bonuses vs. a chosen enemy, dealing with creatures, building castles, forts, and strongholds, and attracting followers. All the Ranger limitations still apply.
In this type of campaign, magical items and treasure of any sort are very, very rare. They may even be nonexistent, as the DM decides.
Magical monsters, equally rare, are especially nasty and fearsome. For example, a dragon encountered in a warriors-only campaign is more like the ferocious, unstoppable engine of death it appears in the myths, and it takes an especially brave St. George to confront one.
And wizards— if wizards are found, they are evil beings who have made pacts and allegiances with nether powers and received their spells from those powers. They're particularly nasty, powerful, and frightening because they have access to powers which the heroes can't even approximate. The heroes must use all their brains and brawn to confront such powerful beings, and will often have to prepare for such a confrontation by finding artifacts, researching the history of the wizard to discover his motives and weaknesses, and so forth.
Strictly Non-Magical World[]
In worlds where there is no magic at all, there can be no genuine Mage characters. (Of course, there can be characters pretending to have magical powers, but they're probably Rogues running some sort of scam operation.) Priests, Rangers, Paladins and Bards exist but have no spells or magical abilities whatsoever; they have only whatever special status their society places on their professions.
Warrior-oriented campaigns set on strictly non-magical worlds are good for a lot of things. By taking the emphasis off magic, you put it on such things as combat, battling the elements, and pure adventure. In such a campaign, only one's wits, physical abilities and skills make the difference between success and failure, life and death. Magic, with all its mystery and all its complications, doesn't ever enter the picture.
This also means that things which would be unimpressive in a magical world can be awesome and mysterious in a non-magical one. A "dragon" may just be a giant dinosaurian beast with no intelligence, no magic spells, and no breath weapon, but it will be terrifying anyway, as the characters have no magic with which to help destroy or defeat it.
Without magic present, characters are never raised from the dead. They must be played more carefully than in games where resurrection is a commonplace event. It might be advisable to start characters out at 3rd level, as described in the Character Creation chapter, so that they'll be a little tougher to compensate for this situation.
Such a campaign is ideal for settings based on historical periods. You could base your AD&D® game campaign on the Crusades, on the era of piracy, on the wars of imperial Rome or ancient Greece, on the conquest of the New World. These are all settings rich in action and mystery, but for which there's little evidence of monsters or magic.